Conformal spectral stability estimates for the Dirichlet Laplacian

Burenkov, Victor, Goldshtein, V. and Ukhlov, A. 2015. Conformal spectral stability estimates for the Dirichlet Laplacian. Mathematische Nachrichten 288 (16) , pp. 1822-1833. 10.1002/mana.201400253

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Abstract

We study the eigenvalue problem for the Dirichlet Laplacian in bounded simply connected plane domains inline image by reducing it, using conformal transformations, to the weighted eigenvalue problem for the Dirichlet Laplacian in the unit disc inline image. This allows us to estimate the variation of the eigenvalues of the Dirichlet Laplacian upon domain perturbation via energy type integrals for a large class of “conformal regular” domains which includes all quasidiscs, i.e. images of the unit disc under quasiconformal homeomorphisms of the plane onto itself. Boundaries of such domains can have any Hausdorff dimension between one and two.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Wiley-Blackwell
ISSN:	0025-584X
Last Modified:	13 Mar 2019 12:58
URI:	https://orca.cardiff.ac.uk/id/eprint/84891

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